A New Method of Solving Multimode Coupled Equations for Analysis of Uniform and Non-Uniform Fiber Bragg Gratings and Its Application to Acoustically Induced Superstructure Modulation

A new and simple mathematical formulation that is employed to analyze numerically coupled-mode equations modeling uniform and non-uniform gratings in optical fiber is investigated. This method would be straightforward and thus beneficial to solve multimode coupled equations in comparison with a previously used fundamental matrix method, and the Runge--Kutta algorithm. The new formulation proposed in this study is applied to calculate transmission and reflection spectra of core mode and higher-order cladding modes of acoustically induced superstructure modulation caused by microbending through fiber Bragg gratings (FBGs). Co-directional and contra-directional couplings based on acoustically induced modulation in FBGs have been discussed for a variety of induced coupling coefficients.